Field-Cycling Relaxometry as a Molecular Rheology Technique: Common Analysis of NMR, Shear Modulus and Dielectric Loss Data of Polymers vs Dendrimers

Analytical Model to Deduce the Conformational and Dynamical Behavior in Dendrimers: A Review

This review utilizes an optimized Rouse-Zimm discrete hydrodynamic model and the preaveraged Oseen tensor, which accurately consider hydrodynamic interactions to study model dendrimers. We report the analytical theories that have been previously developed for the creation of generalized analytical models for dendrimers. These generalized theories were used to assess the conformational and dynamical behavior of the dendrimers. By including stiffness in the bonds, the neglect of excluded volume interactions may be somewhat offset. This is true at least in the case of short spacers. While the topological limitations on the directions and orientations of the individual bond vectors in dendrimers implement semiflexibility, the intensity of these contacts was determined by the potential geometric orientations of the bonds, and later on the excluded volume interactions in dendrimers, which were described in terms of the effective co-volume between nearest non-bonded monomers and modeled using the delta function pseudopotential. With the aid of the models developed, the authors condensed various conformational and dynamic properties of dendrimers that depend on their degree of semiflexibility and the strength of the excluded volume. These analyses came to the conclusion that the flexible dendrimer in one limit and the earlier described freely rotating model of dendrimers in the other constitute a highly generalized way of capturing a wide range of conformations in the developed mathematical model in dendrimers.

Influence of the Chemical Structure on the Mechanical Relaxation of Dendrimers

The rheological properties of macromolecules represent one of the fundamental features of polymer systems which expand the possibilities of using and developing new materials based on them. In this work, we studied the shear-stress relaxation of the second generation PAMAM and PPI dendrimer melts by atomistic molecular dynamics simulation. The time dependences of relaxation modulus G(t) and the frequency dependences of the storage G'(ω) and loss G″(ω) moduli were obtained. The results were compared with the similar dependences for the polycarbosilane (PCS) dendrimer of the same generation. The chemical structure of the dendrimer segments has been found to strongly influence their mechanical relaxation. In particular, it has been shown that hydrogen bonding in PAMAM dendrimers leads to an entanglement of macromolecules and the region is observed where G'(ω) > G″(ω). This slows down the mechanical relaxation and rotational diffusion of macromolecules. We believe that our comprehensive research contributes to the systematization of knowledge about the rheological properties of dendrimers.

Mechanical relaxation of functionalized carbosilane dendrimer melts

Functionalizing the internal structure of classical dendrimers is a new way of tailoring their properties. Using atomistic molecular dynamics simulations, we investigate the rheological behavior of functionalized dendrimer (FD) melts obtained by modifying the branching of carbosilane dendrimers (CSD). The time (relaxation modulus G(t)) and frequency (storage G' and loss G'' moduli) dependencies of the dynamic modulus are obtained. Fourth generation FD melts present a region where G' > G''. In contrast, their non-functionalized counterparts (i.e., classical dendrimers with regular branching) do not show such a region. The comparative analysis of FD and CSD suggests that the internal densification due to functionalization prevents the penetration of branches and causes FD to behave like colloidal particles in a crowded environment. Since CSD have no special interactions, we expect that this effect will be common for other dendrimer macromolecules.

Rheology of Poly(glycidyl methacrylate) Macromolecular Nano Assemblies

A recently reported combined polymerization process of glycidyl methacrylate, mediated by homometallic and heterobimetallic aluminium complexes, naturally produces nano-sized macromolecular assemblies. In this work, the morphological features and the rheological properties of these novel nanoassemblies are studied. The hydrodynamic sizes of the nanoparticles in the solution range from 10 to 40 nm (in numbers), but on a flat surface they adopt a characteristic thin disk shape. The dynamic moduli have been determined in a broad range of temperatures, and the time—temperature superposition applied to obtain master curves of the whole viscoelastic response from the glassy to the terminal regions. The fragility values obtained from the temperature dependence are of m ~40, typical of van de Waals liquids, suggesting a very effective packing of the macromolecular assemblies. The rheological master curves feature a characteristic viscoelastic relaxation with the absence of elastic intermediate plateau, indicating that the systems behaved as un-entangled polymers. The analysis of the linear viscoelastic fingerprint reveals a Zimm-like dynamics at intermediate frequencies typical of unentangled systems. This behaviour resembles that observed in highly functionalized stars, dendrimers, soft colloids and microgels.

Water Dynamics in Whey-Protein-Based Composite Hydrogels by Means of NMR Relaxometry

Whey-protein-isolate-based composite hydrogels with encapsulated black carrot (Daucus carota) extract were prepared by heat-induced gelation. The hydrogels were blended with gum tragacanth, pectin and xanthan gum polysaccharides for modulating their properties. 1H spin-lattice relaxation experiments were performed in a broad frequency range, from 4 kHz to 30 MHz, to obtain insight into the influence of the different polysaccharides and of the presence of black carrot on dynamical properties of water molecules in the hydrogel network. The 1H spin-lattice relaxation data were decomposed into relaxation contributions associated with confined and free water fractions. The population of the confined water fraction and the value of the translation diffusion coefficient of water molecules in the vicinity of the macromolecular network were quantitatively determined on the basis of the relaxation data. Moreover, it was demonstrated that the translation diffusion is highly anisotropic (two-dimensional, 2D).

Viscoelasticity in associating oligomers and polymers: experimental test of the bond lifetime renormalization model

Recent findings that the association bond lifetimes τα* in associating polymers diverge from their supramolecular network relaxation times τc challenge past theories. The bond lifetime renormalization proposed by Rubinstein and coworkers [Stukalin et al., Macromolecules, 2013, 46, 7525] provides a promising explanation. To examine systematically its applicability, we employ shear rheology and dielectric spectroscopy to study telechelic associating polymers with different main chain (polypropylene glycol and polydimethylsiloxane), molecular weight (below entanglement molecular weight) and end groups (amide, and carboxylic acid) which form dimeric associations by hydrogen bonding. The separation between τc (probed by rheology) and τα* (probed by dielectric spectroscopy) strongly increases with chain length as qualitatively predicted by the model. However, to describe the increase quantitatively, a transition from Rouse to reptation dynamics must be assumed. This suggests that dynamics of super-chains must be considered to properly describe the transient network.

Application of proton field-cycling NMR relaxometry for studying translational diffusion in simple liquids and polymer melts

With the availability of commercial field-cycling relaxometers together with progress of home-built instruments nuclear magnetic resonance relaxometry has gained new momentum as a method of investigating the dynamics in viscous liquids and polymer melts. The method provides the frequency dependence of the spin-lattice relaxation rate. In the case of protons, one distinguishes intramolecular and intermolecular relaxation pathways. Whereas the intramolecular contribution prevails at high frequencies and reflects rotational dynamics, the often ignored intermolecular relaxation contribution dominates at low-frequency and provides access to translational dynamics. A universal low-frequencies dispersion law holds which in pure systems allows determining the diffusion coefficient in a straightforward way. In addition, the rotational time constant is extracted from the high-frequency relaxation contribution. This is demonstrated for simple and ionic liquids and for polymer melts.

Spectral shape simplicity of viscous materials

A broad survey of viscoelastic data demonstrates that van der Waals, hydrogen-bonded, and ionic liquids, as well as polymeric, inorganic, and metallic melts share a structural relaxation pattern virtually insensitive to their morphological details. This mechanical simplicity is connected with that characterizing the fast reorientation dynamics prevailing in liquids devoid of a distinguishable secondary susceptibility peak. By these means one is able to uncover a generic spectral pattern which rationalizes the recently reported "universality" of relaxation strength vs stretching of the dielectric response of viscous liquids, significantly broadening the framework in which their relaxation behavior is assessed.

Time Domain NMR in Polymer Science: From the Laboratory to the Industry

Highly controlled polymers and nanostructures are increasingly translated from the lab to the industry. Together with the industrialization of complex systems from renewable sources, a paradigm change in the processing of plastics and rubbers is underway, requiring a new generation of analytical tools. Here, we present the recent developments in time domain NMR (TD-NMR), starting with an introduction of the methods. Several examples illustrate the new take on traditional issues like the measurement of crosslink density in vulcanized rubber or the monitoring of crystallization kinetics, as well as the unique information that can be extracted from multiphase, nanophase and composite materials. Generally, TD-NMR is capable of determining structural parameters that are in agreement with other techniques and with the final macroscopic properties of industrial interest, as well as reveal details on the local homogeneity that are difficult to obtain otherwise. Considering its moderate technical and space requirements of performing, TD-NMR is a good candidate for assisting product and process development in several applications throughout the rubber, plastics, composites and adhesives industry.

Scaling analysis of the viscoelastic response of linear polymers

Viscoelastic response in terms of the complex shear modulus G^*(ω) of the linear polymers poly(ethylene-alt-propylene), poly(isoprene), and poly(butadiene) is studied for molar masses (M) from 3k up to 1000k and over a wide temperature range starting from the glass transition temperature T_g (174 K-373 K). Master curves G'(ωτ_α) and G″(ωτ_α) are constructed for the polymer-specific relaxation. Segmental relaxation occurring close to T_g is independently addressed by single spectra. Altogether, viscoelastic response is effectively studied over 14 decades in frequency. The structural relaxation time τ_α used for scaling is taken from dielectric spectra. We suggest a derivative method for identifying the different power-law regimes and their exponents along G″(ωτ_α) ∝ ω^ε″. The exponent ε″ = ε″(ωτ_α) ≡ d ln G″(ωτ_α)/d ln(ωτ_α) reveals more details compared to conventional analyses and displays high similarity among the polymers. Within a simple scaling model, the original tube-reptation model is extended to include contour length fluctuations (CLFs). The model reproduces all signatures of the quantitative theory by Likhtman and McLeish. The characteristic times and power-law exponents are rediscovered in ε″(ωτ_α). The high-frequency flank of the terminal relaxation closely follows the prediction for CLF (ε″ = -0.25), i.e., G″(ω) ∝ ω^-0.21±0.02. At lower frequencies, a second regime with lower exponent ε″ is observed signaling the crossover to coherent reptation. Application of the full Likhtman-McLeish calculation provides a quantitative interpolation of ε″(ωτ_α) at frequencies below those of the Rouse regime. The derivative method also allows identifying the entanglement time τ_e. However, as the exponent in the Rouse regime (ωτ_e > 1) varies along ε_eRouse = 0.66 ± 0.04 (off the Rouse prediction ε_Rouse = 0.5) and that at ωτ_e < 1 is similar, only a weak manifestation of the crossover at τ_e is found at highest M. Yet, calculating τ_e/τ_α= (M/M_o)², we find good agreement among the polymers when discussing ε″(ωτ_e). The terminal relaxation time τ_t is directly read off from ε″(ωτ_α). Plotting τ_t/τ_e as a function of Z = M/M_e, we find universal behavior as predicted by the TR model. The M dependence crosses over from an exponent significantly larger than 3.0 at intermediate M to an exponent approaching 3.0 at highest M in agreement with previous reports. The frequency of the minimum in G″(ωτ_α) scales as τ_min ∝ M^1.0±0.1. An M-independent frequency marks the crossover to glassy relaxation at the highest frequencies. Independent of the amplitude of G″(ω), which may be related to sample-to-sample differences, the derivative method is a versatile tool to provide a detailed phenomenological analysis of the viscoelastic response of complex liquids.

NMR studies of excluded volume interactions in peptide dendrimers

Peptide dendrimers are good candidates for diverse biomedical applications due to their biocompatibility and low toxicity. The local orientational mobility of groups with different radial localization inside dendrimers is important characteristic for drug and gene delivery, synthesis of nanoparticles, and other specific purposes. In this paper we focus on the validation of two theoretical assumptions for dendrimers: (i) independence of NMR relaxations on excluded volume effects and (ii) similarity of mobilities of side and terminal segments of dendrimers. For this purpose we study 1H NMR spin-lattice relaxation time, T1H, of two similar peptide dendrimers of the second generation, with and without side fragments in their inner segments. Temperature dependences of 1/T1H in the temperature range from 283 to 343 K were measured for inner and terminal groups of the dendrimers dissolved in deuterated water. We have shown that the 1/T1H temperature dependences of inner groups for both dendrimers (with and without side fragments) practically coincide despite different densities of atoms inside these dendrimers. This result confirms the first theoretical assumption. The second assumption is confirmed by the 1/T1H temperature dependences of terminal groups which are similar for both dendrimers.

Field-cycling NMR experiments in an ultra-wide magnetic field range: relaxation and coherent polarization transfer

An experimental method is described allowing fast field-cycling Nuclear Magnetic Resonance (NMR) experiments over a wide range of magnetic fields from 5 nT to 10 T. The method makes use of a hybrid technique: the high field range is covered by positioning the sample in the inhomogeneous stray field of the NMR spectrometer magnet. For fields below 2 mT a magnetic shield is mounted on top of the spectrometer; inside the shield the magnetic field is controlled by a specially designed coil system. This combination allows us to measure T1-relaxation times and nuclear Overhauser effect parameters over the full range in a routine way. For coupled proton-carbon spin systems relaxation with a common T1 is found at low fields, where the spins are "strongly coupled". In some cases, experiments at ultralow fields provide access to heteronuclear long-lived spin states. Efficient coherent polarization transfer is seen for proton-carbon spin systems at ultralow fields as follows from the observation of quantum oscillations in the polarization evolution. Applications to analysis and the manipulation of heteronuclear spin systems are discussed.

Slow rheological mode in glycerol and glycerol–water mixtures

Glycerol–water mixtures were studied at molar concentrations ranging from x_gly = 1 (neat glycerol) to x_gly = 0.3 using shear mechanical spectroscopy.

Investigation of Melts of Polybutylcarbosilane Dendrimers by 1H NMR Spectroscopy

Melts of polybutylcarbosilane (PBC) dendrimers from third (G3) up to sixth (G6) generations are investigated by ¹H NMR spectroscopy in a wide temperature range up to 493 K. At room temperature, NMR spectra of G3-G5 dendrimers exhibit resolved, solution-like spectra (“liquid” phase). In contrast, the spectrum of the G6 dendrimer is characterized by a single unresolved broad line at whole temperature range, which supports the presence of an anomalous phase state of G6 at temperatures higher than glass transition temperature. For the first time, an unexpected transition of G5 dendrimer from a molecular liquid state to an anomalous state/phase upon temperature increase has been detected using NMR data. Specifically, an additional wide background line appears in the G5 spectrum above 473 K, and this line corresponds to a G5 state characterized by restricted molecular mobility, i.e., a state similar to the “anomalous” phase of G6 melt. The fraction of the G5 dendrimers in “anomalous” phase at 493 K is approximately 40%. Analysis of the spectral shapes suggests that changes in the G5 dendrimers are reversible with temperature.

Local orientational mobility in regular hyperbranched polymers

We study the dynamics of local bond orientation in regular hyperbranched polymers modeled by Vicsek fractals. The local dynamics is investigated through the temporal autocorrelation functions of single bonds and the corresponding relaxation forms of the complex dielectric susceptibility. We show that the dynamic behavior of single segments depends on their remoteness from the periphery rather than on the size of the whole macromolecule. Remarkably, the dynamics of the core segments (which are most remote from the periphery) shows a scaling behavior that differs from the dynamics obtained after structural average. We analyze the most relevant processes of single segment motion and provide an analytic approximation for the corresponding relaxation times. Furthermore, we describe an iterative method to calculate the orientational dynamics in the case of very large macromolecular sizes.

Dynamics of internally functionalized dendrimers

The internally functionalized dendrimers are novel polymers that differ from conventional dendrimers by having additional functional units which do not branch out further. We investigate the dynamics of these structures with the inclusion of local semiflexibility and analyze their eigenmodes. The functionalized units clearly manifest themselves leading to a group of eigenvalues which are not present for homogeneous dendrimers. This part of the spectrum reveals itself in the local relaxation, leading to a corresponding process in the imaginary part of the complex dielectric susceptibility.